NBHM (National Board for Higher Mathematics) MSc and MA Mathematics: Questions 35  42 of 101
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Question number: 35
Appeared in Year: 2012
Question
Let be a sequence of functions defined on . Determine . For each the following.
Choices
Choice (4)  Response  

a. 


b. 


c. 


d.  All a. , b. and c. are correct 

Question number: 36
Appeared in Year: 2013
Describe in Detail
Find the area of the polygon whose vertices are represented in the complex plane by the eighth roots of unity.
Explanation
In triangle OAB
area of triangle
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Question number: 37
Appeared in Year: 2011
Describe in Detail
Evaluate
Explanation
And
This is exponential form
Using the Result:
If
Then
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Question number: 38
Appeared in Year: 2007
Describe in Detail
Find the Minimum value of the function:
Explanation
Here
Step I:
Step II: Let us solve
i. e
and
we get
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Question number: 39
Appeared in Year: 2005
Describe in Detail
Let denote the seventh roots of unity. Evaluate
Explanation
Let x be nth root of unity. Then
(Where k is an integer)
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Question number: 40
Appeared in Year: 2006
Describe in Detail
What is the relation between the height and radius of a right circular cylinder of fixed volume and Minimal Total surface area?
Explanation
Here given that is the radius of the base of right circular cylinder and its height. is the volume and Let be the total surface area.
Also
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Question number: 41
Appeared in Year: 2012
Describe in Detail
Find the area of the pentagon whose vertices are the fifth root of unity in the complex plane.
Explanation
To find fifth root of unity.
Let
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Question number: 42
Appeared in Year: 2015
Describe in Detail
Does the integral exist? If it exists give its value.
Explanation
Yes, its value is…
Note that is not defined for . Here we can write;
(Integration by parts)
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